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%I #13 May 28 2021 11:06:00
%S 0,1,0,0,0,0,1,0,1,0,1,0,0,0,1,0,0,0,1,0,0,0,0,1,0,1,1,0,0,0,0,1,0,1,
%T 1,0,0,0,0,1,0,1,0,1,0,0,0,1,1,0,0,0,0,1,0,1,0,1,0,0,0,1,1,0,0,0,0,1,
%U 0,1,0,1,0,0,0,1,0,0,0,1,0,0,0,0,1,0
%N Fixed point of the mapping 00->0101, 10->1000, starting with 00.
%H Clark Kimberling, <a href="/A288596/b288596.txt">Table of n, a(n) for n = 1..10000</a>
%e Iterates, starting with 00:
%e 00
%e 0101
%e 010001
%e 0100001011
%e 0100001010100011
%e 0100001010100010001000010111
%e Conjecture: the number of letters (0's and 1's) in the n-th iterate is given by A288599(n).
%t s = {0, 0}; w[0] = StringJoin[Map[ToString, s]];
%t w[n_] := StringReplace[w[n - 1], {"00" -> "0101", "10" -> "1000"}]
%t Table[w[n], {n, 0, 8}]
%t st = ToCharacterCode[w[11]] - 48 (* A288596 *)
%t Flatten[Position[st, 0]] (* A288597 *)
%t Flatten[Position[st, 1]] (* A288598 *)
%t Table[StringLength[w[n]], {n, 1, 35}] (* A288599 conjectured *)
%Y Cf. A288597, A288598, A288599.
%K nonn,easy
%O 1
%A _Clark Kimberling_, Jun 14 2017
%E Definition corrected by _Georg Fischer_, May 28 2021
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